Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2

Percentage Accurate: 56.2% → 83.1%

Time: 10.0s

Alternatives: 14

Speedup: 2.0×

Specification

Math

\[\begin{array}{l} \\ \frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (/
  (+ (* (+ (* (+ (* (+ (* x y) z) y) 27464.7644705) y) 230661.510616) y) t)
  (+ (* (+ (* (+ (* (+ y a) y) b) y) c) y) i)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	return ((((((((x * y) + z) * y) + 27464.7644705) * y) + 230661.510616) * y) + t) / (((((((y + a) * y) + b) * y) + c) * y) + i);
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a, b, c, i)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    code = ((((((((x * y) + z) * y) + 27464.7644705d0) * y) + 230661.510616d0) * y) + t) / (((((((y + a) * y) + b) * y) + c) * y) + i)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	return ((((((((x * y) + z) * y) + 27464.7644705) * y) + 230661.510616) * y) + t) / (((((((y + a) * y) + b) * y) + c) * y) + i);
}

Python

def code(x, y, z, t, a, b, c, i):
	return ((((((((x * y) + z) * y) + 27464.7644705) * y) + 230661.510616) * y) + t) / (((((((y + a) * y) + b) * y) + c) * y) + i)

Julia

function code(x, y, z, t, a, b, c, i)
	return Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(x * y) + z) * y) + 27464.7644705) * y) + 230661.510616) * y) + t) / Float64(Float64(Float64(Float64(Float64(Float64(Float64(y + a) * y) + b) * y) + c) * y) + i))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i)
	tmp = ((((((((x * y) + z) * y) + 27464.7644705) * y) + 230661.510616) * y) + t) / (((((((y + a) * y) + b) * y) + c) * y) + i);
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := N[(N[(N[(N[(N[(N[(N[(N[(N[(x * y), $MachinePrecision] + z), $MachinePrecision] * y), $MachinePrecision] + 27464.7644705), $MachinePrecision] * y), $MachinePrecision] + 230661.510616), $MachinePrecision] * y), $MachinePrecision] + t), $MachinePrecision] / N[(N[(N[(N[(N[(N[(N[(y + a), $MachinePrecision] * y), $MachinePrecision] + b), $MachinePrecision] * y), $MachinePrecision] + c), $MachinePrecision] * y), $MachinePrecision] + i), $MachinePrecision]), $MachinePrecision]

Initial Program: 56.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (/
  (+ (* (+ (* (+ (* (+ (* x y) z) y) 27464.7644705) y) 230661.510616) y) t)
  (+ (* (+ (* (+ (* (+ y a) y) b) y) c) y) i)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	return ((((((((x * y) + z) * y) + 27464.7644705) * y) + 230661.510616) * y) + t) / (((((((y + a) * y) + b) * y) + c) * y) + i);
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a, b, c, i)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    code = ((((((((x * y) + z) * y) + 27464.7644705d0) * y) + 230661.510616d0) * y) + t) / (((((((y + a) * y) + b) * y) + c) * y) + i)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	return ((((((((x * y) + z) * y) + 27464.7644705) * y) + 230661.510616) * y) + t) / (((((((y + a) * y) + b) * y) + c) * y) + i);
}

Python

def code(x, y, z, t, a, b, c, i):
	return ((((((((x * y) + z) * y) + 27464.7644705) * y) + 230661.510616) * y) + t) / (((((((y + a) * y) + b) * y) + c) * y) + i)

Julia

function code(x, y, z, t, a, b, c, i)
	return Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(x * y) + z) * y) + 27464.7644705) * y) + 230661.510616) * y) + t) / Float64(Float64(Float64(Float64(Float64(Float64(Float64(y + a) * y) + b) * y) + c) * y) + i))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i)
	tmp = ((((((((x * y) + z) * y) + 27464.7644705) * y) + 230661.510616) * y) + t) / (((((((y + a) * y) + b) * y) + c) * y) + i);
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := N[(N[(N[(N[(N[(N[(N[(N[(N[(x * y), $MachinePrecision] + z), $MachinePrecision] * y), $MachinePrecision] + 27464.7644705), $MachinePrecision] * y), $MachinePrecision] + 230661.510616), $MachinePrecision] * y), $MachinePrecision] + t), $MachinePrecision] / N[(N[(N[(N[(N[(N[(N[(y + a), $MachinePrecision] * y), $MachinePrecision] + b), $MachinePrecision] * y), $MachinePrecision] + c), $MachinePrecision] * y), $MachinePrecision] + i), $MachinePrecision]), $MachinePrecision]

Alternative 1: 83.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t\\ t_2 := \frac{t\_1}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\\ t_3 := \mathsf{fma}\left(a + y, y, b\right)\\ t_4 := \mathsf{fma}\left(\mathsf{fma}\left(t\_3, y, c\right), y, i\right)\\ \mathbf{if}\;t\_2 \leq 2 \cdot 10^{+294}:\\ \;\;\;\;\frac{t\_1}{\mathsf{fma}\left(y, c, \left(t\_3 \cdot y\right) \cdot y\right) + i}\\ \mathbf{elif}\;t\_2 \leq \infty:\\ \;\;\;\;\left(-x\right) \cdot \left(\frac{-\left(y \cdot y\right) \cdot \left(y \cdot y\right)}{t\_4} + \left(-\frac{\frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z, y, 27464.7644705\right), y, 230661.510616\right), y, t\right)}{t\_4}}{x}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(-\frac{\left(-z\right) - \left(-a\right) \cdot x}{y}\right) + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1
         (+
          (* (+ (* (+ (* (+ (* x y) z) y) 27464.7644705) y) 230661.510616) y)
          t))
        (t_2 (/ t_1 (+ (* (+ (* (+ (* (+ y a) y) b) y) c) y) i)))
        (t_3 (fma (+ a y) y b))
        (t_4 (fma (fma t_3 y c) y i)))
   (if (<= t_2 2e+294)
     (/ t_1 (+ (fma y c (* (* t_3 y) y)) i))
     (if (<= t_2 INFINITY)
       (*
        (- x)
        (+
         (/ (- (* (* y y) (* y y))) t_4)
         (-
          (/
           (/ (fma (fma (fma z y 27464.7644705) y 230661.510616) y t) t_4)
           x))))
       (+ (- (/ (- (- z) (* (- a) x)) y)) x)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (((((((x * y) + z) * y) + 27464.7644705) * y) + 230661.510616) * y) + t;
	double t_2 = t_1 / (((((((y + a) * y) + b) * y) + c) * y) + i);
	double t_3 = fma((a + y), y, b);
	double t_4 = fma(fma(t_3, y, c), y, i);
	double tmp;
	if (t_2 <= 2e+294) {
		tmp = t_1 / (fma(y, c, ((t_3 * y) * y)) + i);
	} else if (t_2 <= ((double) INFINITY)) {
		tmp = -x * ((-((y * y) * (y * y)) / t_4) + -((fma(fma(fma(z, y, 27464.7644705), y, 230661.510616), y, t) / t_4) / x));
	} else {
		tmp = -((-z - (-a * x)) / y) + x;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(x * y) + z) * y) + 27464.7644705) * y) + 230661.510616) * y) + t)
	t_2 = Float64(t_1 / Float64(Float64(Float64(Float64(Float64(Float64(Float64(y + a) * y) + b) * y) + c) * y) + i))
	t_3 = fma(Float64(a + y), y, b)
	t_4 = fma(fma(t_3, y, c), y, i)
	tmp = 0.0
	if (t_2 <= 2e+294)
		tmp = Float64(t_1 / Float64(fma(y, c, Float64(Float64(t_3 * y) * y)) + i));
	elseif (t_2 <= Inf)
		tmp = Float64(Float64(-x) * Float64(Float64(Float64(-Float64(Float64(y * y) * Float64(y * y))) / t_4) + Float64(-Float64(Float64(fma(fma(fma(z, y, 27464.7644705), y, 230661.510616), y, t) / t_4) / x))));
	else
		tmp = Float64(Float64(-Float64(Float64(Float64(-z) - Float64(Float64(-a) * x)) / y)) + x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(N[(N[(N[(N[(N[(N[(x * y), $MachinePrecision] + z), $MachinePrecision] * y), $MachinePrecision] + 27464.7644705), $MachinePrecision] * y), $MachinePrecision] + 230661.510616), $MachinePrecision] * y), $MachinePrecision] + t), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 / N[(N[(N[(N[(N[(N[(N[(y + a), $MachinePrecision] * y), $MachinePrecision] + b), $MachinePrecision] * y), $MachinePrecision] + c), $MachinePrecision] * y), $MachinePrecision] + i), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(a + y), $MachinePrecision] * y + b), $MachinePrecision]}, Block[{t$95$4 = N[(N[(t$95$3 * y + c), $MachinePrecision] * y + i), $MachinePrecision]}, If[LessEqual[t$95$2, 2e+294], N[(t$95$1 / N[(N[(y * c + N[(N[(t$95$3 * y), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision] + i), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, Infinity], N[((-x) * N[(N[((-N[(N[(y * y), $MachinePrecision] * N[(y * y), $MachinePrecision]), $MachinePrecision]) / t$95$4), $MachinePrecision] + (-N[(N[(N[(N[(N[(z * y + 27464.7644705), $MachinePrecision] * y + 230661.510616), $MachinePrecision] * y + t), $MachinePrecision] / t$95$4), $MachinePrecision] / x), $MachinePrecision])), $MachinePrecision]), $MachinePrecision], N[((-N[(N[((-z) - N[((-a) * x), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]) + x), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x y) z) y) #s(literal 54929528941/2000000 binary64)) y) #s(literal 28832688827/125000 binary64)) y) t) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 y a) y) b) y) c) y) i)) < 2.00000000000000013e294

   1. Initial program 92.0%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   2. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \frac{\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y + \frac{28832688827}{125000}\right) \cdot y + t}{\color{blue}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y} + i} \]

      2. lift-+.f64 N/A

         \[\leadsto \frac{\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y + \frac{28832688827}{125000}\right) \cdot y + t}{\color{blue}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right)} \cdot y + i} \]

      3. lift-*.f64 N/A

         \[\leadsto \frac{\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y + \frac{28832688827}{125000}\right) \cdot y + t}{\left(\color{blue}{\left(\left(y + a\right) \cdot y + b\right) \cdot y} + c\right) \cdot y + i} \]

      4. lift-+.f64 N/A

         \[\leadsto \frac{\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y + \frac{28832688827}{125000}\right) \cdot y + t}{\left(\color{blue}{\left(\left(y + a\right) \cdot y + b\right)} \cdot y + c\right) \cdot y + i} \]

      5. lift-*.f64 N/A

         \[\leadsto \frac{\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y + \frac{28832688827}{125000}\right) \cdot y + t}{\left(\left(\color{blue}{\left(y + a\right) \cdot y} + b\right) \cdot y + c\right) \cdot y + i} \]

      6. lift-+.f64 N/A

         \[\leadsto \frac{\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y + \frac{28832688827}{125000}\right) \cdot y + t}{\left(\left(\color{blue}{\left(y + a\right)} \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

      7. +-commutative N/A

         \[\leadsto \frac{\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y + \frac{28832688827}{125000}\right) \cdot y + t}{\left(\color{blue}{\left(b + \left(y + a\right) \cdot y\right)} \cdot y + c\right) \cdot y + i} \]

      8. *-commutative N/A

         \[\leadsto \frac{\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y + \frac{28832688827}{125000}\right) \cdot y + t}{\left(\left(b + \color{blue}{y \cdot \left(y + a\right)}\right) \cdot y + c\right) \cdot y + i} \]

      9. +-commutative N/A

         \[\leadsto \frac{\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y + \frac{28832688827}{125000}\right) \cdot y + t}{\left(\left(b + y \cdot \color{blue}{\left(a + y\right)}\right) \cdot y + c\right) \cdot y + i} \]

      10. *-commutative N/A

          \[\leadsto \frac{\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y + \frac{28832688827}{125000}\right) \cdot y + t}{\left(\color{blue}{y \cdot \left(b + y \cdot \left(a + y\right)\right)} + c\right) \cdot y + i} \]

      11. +-commutative N/A

          \[\leadsto \frac{\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y + \frac{28832688827}{125000}\right) \cdot y + t}{\color{blue}{\left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} \cdot y + i} \]

      12. *-commutative N/A

          \[\leadsto \frac{\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y + \frac{28832688827}{125000}\right) \cdot y + t}{\color{blue}{y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} + i} \]

      13. distribute-rgt-in N/A

          \[\leadsto \frac{\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y + \frac{28832688827}{125000}\right) \cdot y + t}{\color{blue}{\left(c \cdot y + \left(y \cdot \left(b + y \cdot \left(a + y\right)\right)\right) \cdot y\right)} + i} \]

      14. *-commutative N/A

          \[\leadsto \frac{\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y + \frac{28832688827}{125000}\right) \cdot y + t}{\left(\color{blue}{y \cdot c} + \left(y \cdot \left(b + y \cdot \left(a + y\right)\right)\right) \cdot y\right) + i} \]

      15. lower-fma.f64 N/A

          \[\leadsto \frac{\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y + \frac{28832688827}{125000}\right) \cdot y + t}{\color{blue}{\mathsf{fma}\left(y, c, \left(y \cdot \left(b + y \cdot \left(a + y\right)\right)\right) \cdot y\right)} + i} \]

   3. Applied rewrites 92.0%

      \[\leadsto \frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\color{blue}{\mathsf{fma}\left(y, c, \left(\mathsf{fma}\left(a + y, y, b\right) \cdot y\right) \cdot y\right)} + i} \]

   if 2.00000000000000013e294 < (/.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x y) z) y) #s(literal 54929528941/2000000 binary64)) y) #s(literal 28832688827/125000 binary64)) y) t) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 y a) y) b) y) c) y) i)) < +inf.0

   1. Initial program 55.6%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

   2. Taylor expanded in x around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(x \cdot \left(-1 \cdot \frac{\frac{t}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} + \frac{y \cdot \left(\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot z\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}}{x} + -1 \cdot \frac{{y}^{4}}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}\right)\right)} \]

   4. Applied rewrites 79.5%

      \[\leadsto \color{blue}{\left(-x\right) \cdot \left(\frac{-\left(y \cdot y\right) \cdot \left(y \cdot y\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(a + y, y, b\right), y, c\right), y, i\right)} + \left(-\frac{\frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z, y, 27464.7644705\right), y, 230661.510616\right), y, t\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(a + y, y, b\right), y, c\right), y, i\right)}}{x}\right)\right)} \]

   if +inf.0 < (/.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x y) z) y) #s(literal 54929528941/2000000 binary64)) y) #s(literal 28832688827/125000 binary64)) y) t) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 y a) y) b) y) c) y) i))

   1. Initial program 0.0%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

   2. Taylor expanded in y around -inf

      \[\leadsto \color{blue}{x + -1 \cdot \frac{-1 \cdot z - -1 \cdot \left(a \cdot x\right)}{y}} \]
   3. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto -1 \cdot \frac{-1 \cdot z - -1 \cdot \left(a \cdot x\right)}{y} + \color{blue}{x} \]

      2. lower-+.f64 N/A

         \[\leadsto -1 \cdot \frac{-1 \cdot z - -1 \cdot \left(a \cdot x\right)}{y} + \color{blue}{x} \]

      3. mul-1-neg N/A

         \[\leadsto \left(\mathsf{neg}\left(\frac{-1 \cdot z - -1 \cdot \left(a \cdot x\right)}{y}\right)\right) + x \]

      4. lower-neg.f64 N/A

         \[\leadsto \left(-\frac{-1 \cdot z - -1 \cdot \left(a \cdot x\right)}{y}\right) + x \]

      5. lower-/.f64 N/A

         \[\leadsto \left(-\frac{-1 \cdot z - -1 \cdot \left(a \cdot x\right)}{y}\right) + x \]

      6. lower--.f64 N/A

         \[\leadsto \left(-\frac{-1 \cdot z - -1 \cdot \left(a \cdot x\right)}{y}\right) + x \]

      7. mul-1-neg N/A

         \[\leadsto \left(-\frac{\left(\mathsf{neg}\left(z\right)\right) - -1 \cdot \left(a \cdot x\right)}{y}\right) + x \]

      8. lower-neg.f64 N/A

         \[\leadsto \left(-\frac{\left(-z\right) - -1 \cdot \left(a \cdot x\right)}{y}\right) + x \]

      9. associate-*r* N/A

         \[\leadsto \left(-\frac{\left(-z\right) - \left(-1 \cdot a\right) \cdot x}{y}\right) + x \]

      10. mul-1-neg N/A

          \[\leadsto \left(-\frac{\left(-z\right) - \left(\mathsf{neg}\left(a\right)\right) \cdot x}{y}\right) + x \]

      11. lower-*.f64 N/A

          \[\leadsto \left(-\frac{\left(-z\right) - \left(\mathsf{neg}\left(a\right)\right) \cdot x}{y}\right) + x \]

      12. lower-neg.f64 69.6

          \[\leadsto \left(-\frac{\left(-z\right) - \left(-a\right) \cdot x}{y}\right) + x \]

   4. Applied rewrites 69.6%

      \[\leadsto \color{blue}{\left(-\frac{\left(-z\right) - \left(-a\right) \cdot x}{y}\right) + x} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 2: 82.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t\\ \mathbf{if}\;\frac{t\_1}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \leq \infty:\\ \;\;\;\;\frac{t\_1}{\mathsf{fma}\left(y, c, \left(\mathsf{fma}\left(a + y, y, b\right) \cdot y\right) \cdot y\right) + i}\\ \mathbf{else}:\\ \;\;\;\;\left(-\frac{\left(-z\right) - \left(-a\right) \cdot x}{y}\right) + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1
         (+
          (* (+ (* (+ (* (+ (* x y) z) y) 27464.7644705) y) 230661.510616) y)
          t)))
   (if (<= (/ t_1 (+ (* (+ (* (+ (* (+ y a) y) b) y) c) y) i)) INFINITY)
     (/ t_1 (+ (fma y c (* (* (fma (+ a y) y b) y) y)) i))
     (+ (- (/ (- (- z) (* (- a) x)) y)) x))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (((((((x * y) + z) * y) + 27464.7644705) * y) + 230661.510616) * y) + t;
	double tmp;
	if ((t_1 / (((((((y + a) * y) + b) * y) + c) * y) + i)) <= ((double) INFINITY)) {
		tmp = t_1 / (fma(y, c, ((fma((a + y), y, b) * y) * y)) + i);
	} else {
		tmp = -((-z - (-a * x)) / y) + x;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(x * y) + z) * y) + 27464.7644705) * y) + 230661.510616) * y) + t)
	tmp = 0.0
	if (Float64(t_1 / Float64(Float64(Float64(Float64(Float64(Float64(Float64(y + a) * y) + b) * y) + c) * y) + i)) <= Inf)
		tmp = Float64(t_1 / Float64(fma(y, c, Float64(Float64(fma(Float64(a + y), y, b) * y) * y)) + i));
	else
		tmp = Float64(Float64(-Float64(Float64(Float64(-z) - Float64(Float64(-a) * x)) / y)) + x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(N[(N[(N[(N[(N[(N[(x * y), $MachinePrecision] + z), $MachinePrecision] * y), $MachinePrecision] + 27464.7644705), $MachinePrecision] * y), $MachinePrecision] + 230661.510616), $MachinePrecision] * y), $MachinePrecision] + t), $MachinePrecision]}, If[LessEqual[N[(t$95$1 / N[(N[(N[(N[(N[(N[(N[(y + a), $MachinePrecision] * y), $MachinePrecision] + b), $MachinePrecision] * y), $MachinePrecision] + c), $MachinePrecision] * y), $MachinePrecision] + i), $MachinePrecision]), $MachinePrecision], Infinity], N[(t$95$1 / N[(N[(y * c + N[(N[(N[(N[(a + y), $MachinePrecision] * y + b), $MachinePrecision] * y), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision] + i), $MachinePrecision]), $MachinePrecision], N[((-N[(N[((-z) - N[((-a) * x), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]) + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x y) z) y) #s(literal 54929528941/2000000 binary64)) y) #s(literal 28832688827/125000 binary64)) y) t) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 y a) y) b) y) c) y) i)) < +inf.0

   1. Initial program 90.2%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   2. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \frac{\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y + \frac{28832688827}{125000}\right) \cdot y + t}{\color{blue}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y} + i} \]

      2. lift-+.f64 N/A

         \[\leadsto \frac{\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y + \frac{28832688827}{125000}\right) \cdot y + t}{\color{blue}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right)} \cdot y + i} \]

      3. lift-*.f64 N/A

         \[\leadsto \frac{\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y + \frac{28832688827}{125000}\right) \cdot y + t}{\left(\color{blue}{\left(\left(y + a\right) \cdot y + b\right) \cdot y} + c\right) \cdot y + i} \]

      4. lift-+.f64 N/A

         \[\leadsto \frac{\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y + \frac{28832688827}{125000}\right) \cdot y + t}{\left(\color{blue}{\left(\left(y + a\right) \cdot y + b\right)} \cdot y + c\right) \cdot y + i} \]

      5. lift-*.f64 N/A

         \[\leadsto \frac{\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y + \frac{28832688827}{125000}\right) \cdot y + t}{\left(\left(\color{blue}{\left(y + a\right) \cdot y} + b\right) \cdot y + c\right) \cdot y + i} \]

      6. lift-+.f64 N/A

         \[\leadsto \frac{\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y + \frac{28832688827}{125000}\right) \cdot y + t}{\left(\left(\color{blue}{\left(y + a\right)} \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

      7. +-commutative N/A

         \[\leadsto \frac{\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y + \frac{28832688827}{125000}\right) \cdot y + t}{\left(\color{blue}{\left(b + \left(y + a\right) \cdot y\right)} \cdot y + c\right) \cdot y + i} \]

      8. *-commutative N/A

         \[\leadsto \frac{\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y + \frac{28832688827}{125000}\right) \cdot y + t}{\left(\left(b + \color{blue}{y \cdot \left(y + a\right)}\right) \cdot y + c\right) \cdot y + i} \]

      9. +-commutative N/A

         \[\leadsto \frac{\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y + \frac{28832688827}{125000}\right) \cdot y + t}{\left(\left(b + y \cdot \color{blue}{\left(a + y\right)}\right) \cdot y + c\right) \cdot y + i} \]

      10. *-commutative N/A

          \[\leadsto \frac{\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y + \frac{28832688827}{125000}\right) \cdot y + t}{\left(\color{blue}{y \cdot \left(b + y \cdot \left(a + y\right)\right)} + c\right) \cdot y + i} \]

      11. +-commutative N/A

          \[\leadsto \frac{\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y + \frac{28832688827}{125000}\right) \cdot y + t}{\color{blue}{\left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} \cdot y + i} \]

      12. *-commutative N/A

          \[\leadsto \frac{\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y + \frac{28832688827}{125000}\right) \cdot y + t}{\color{blue}{y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} + i} \]

      13. distribute-rgt-in N/A

          \[\leadsto \frac{\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y + \frac{28832688827}{125000}\right) \cdot y + t}{\color{blue}{\left(c \cdot y + \left(y \cdot \left(b + y \cdot \left(a + y\right)\right)\right) \cdot y\right)} + i} \]

      14. *-commutative N/A

          \[\leadsto \frac{\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y + \frac{28832688827}{125000}\right) \cdot y + t}{\left(\color{blue}{y \cdot c} + \left(y \cdot \left(b + y \cdot \left(a + y\right)\right)\right) \cdot y\right) + i} \]

      15. lower-fma.f64 N/A

          \[\leadsto \frac{\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y + \frac{28832688827}{125000}\right) \cdot y + t}{\color{blue}{\mathsf{fma}\left(y, c, \left(y \cdot \left(b + y \cdot \left(a + y\right)\right)\right) \cdot y\right)} + i} \]

   3. Applied rewrites 90.2%

      \[\leadsto \frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\color{blue}{\mathsf{fma}\left(y, c, \left(\mathsf{fma}\left(a + y, y, b\right) \cdot y\right) \cdot y\right)} + i} \]

   if +inf.0 < (/.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x y) z) y) #s(literal 54929528941/2000000 binary64)) y) #s(literal 28832688827/125000 binary64)) y) t) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 y a) y) b) y) c) y) i))

   1. Initial program 0.0%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

   2. Taylor expanded in y around -inf

      \[\leadsto \color{blue}{x + -1 \cdot \frac{-1 \cdot z - -1 \cdot \left(a \cdot x\right)}{y}} \]
   3. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto -1 \cdot \frac{-1 \cdot z - -1 \cdot \left(a \cdot x\right)}{y} + \color{blue}{x} \]

      2. lower-+.f64 N/A

         \[\leadsto -1 \cdot \frac{-1 \cdot z - -1 \cdot \left(a \cdot x\right)}{y} + \color{blue}{x} \]

      3. mul-1-neg N/A

         \[\leadsto \left(\mathsf{neg}\left(\frac{-1 \cdot z - -1 \cdot \left(a \cdot x\right)}{y}\right)\right) + x \]

      4. lower-neg.f64 N/A

         \[\leadsto \left(-\frac{-1 \cdot z - -1 \cdot \left(a \cdot x\right)}{y}\right) + x \]

      5. lower-/.f64 N/A

         \[\leadsto \left(-\frac{-1 \cdot z - -1 \cdot \left(a \cdot x\right)}{y}\right) + x \]

      6. lower--.f64 N/A

         \[\leadsto \left(-\frac{-1 \cdot z - -1 \cdot \left(a \cdot x\right)}{y}\right) + x \]

      7. mul-1-neg N/A

         \[\leadsto \left(-\frac{\left(\mathsf{neg}\left(z\right)\right) - -1 \cdot \left(a \cdot x\right)}{y}\right) + x \]

      8. lower-neg.f64 N/A

         \[\leadsto \left(-\frac{\left(-z\right) - -1 \cdot \left(a \cdot x\right)}{y}\right) + x \]

      9. associate-*r* N/A

         \[\leadsto \left(-\frac{\left(-z\right) - \left(-1 \cdot a\right) \cdot x}{y}\right) + x \]

      10. mul-1-neg N/A

          \[\leadsto \left(-\frac{\left(-z\right) - \left(\mathsf{neg}\left(a\right)\right) \cdot x}{y}\right) + x \]

      11. lower-*.f64 N/A

          \[\leadsto \left(-\frac{\left(-z\right) - \left(\mathsf{neg}\left(a\right)\right) \cdot x}{y}\right) + x \]

      12. lower-neg.f64 69.6

          \[\leadsto \left(-\frac{\left(-z\right) - \left(-a\right) \cdot x}{y}\right) + x \]

   4. Applied rewrites 69.6%

      \[\leadsto \color{blue}{\left(-\frac{\left(-z\right) - \left(-a\right) \cdot x}{y}\right) + x} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 3: 82.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\\ \mathbf{if}\;t\_1 \leq \infty:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\left(-\frac{\left(-z\right) - \left(-a\right) \cdot x}{y}\right) + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1
         (/
          (+
           (* (+ (* (+ (* (+ (* x y) z) y) 27464.7644705) y) 230661.510616) y)
           t)
          (+ (* (+ (* (+ (* (+ y a) y) b) y) c) y) i))))
   (if (<= t_1 INFINITY) t_1 (+ (- (/ (- (- z) (* (- a) x)) y)) x))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = ((((((((x * y) + z) * y) + 27464.7644705) * y) + 230661.510616) * y) + t) / (((((((y + a) * y) + b) * y) + c) * y) + i);
	double tmp;
	if (t_1 <= ((double) INFINITY)) {
		tmp = t_1;
	} else {
		tmp = -((-z - (-a * x)) / y) + x;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = ((((((((x * y) + z) * y) + 27464.7644705) * y) + 230661.510616) * y) + t) / (((((((y + a) * y) + b) * y) + c) * y) + i);
	double tmp;
	if (t_1 <= Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else {
		tmp = -((-z - (-a * x)) / y) + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = ((((((((x * y) + z) * y) + 27464.7644705) * y) + 230661.510616) * y) + t) / (((((((y + a) * y) + b) * y) + c) * y) + i)
	tmp = 0
	if t_1 <= math.inf:
		tmp = t_1
	else:
		tmp = -((-z - (-a * x)) / y) + x
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(x * y) + z) * y) + 27464.7644705) * y) + 230661.510616) * y) + t) / Float64(Float64(Float64(Float64(Float64(Float64(Float64(y + a) * y) + b) * y) + c) * y) + i))
	tmp = 0.0
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = Float64(Float64(-Float64(Float64(Float64(-z) - Float64(Float64(-a) * x)) / y)) + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = ((((((((x * y) + z) * y) + 27464.7644705) * y) + 230661.510616) * y) + t) / (((((((y + a) * y) + b) * y) + c) * y) + i);
	tmp = 0.0;
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = -((-z - (-a * x)) / y) + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(N[(N[(N[(N[(N[(N[(N[(x * y), $MachinePrecision] + z), $MachinePrecision] * y), $MachinePrecision] + 27464.7644705), $MachinePrecision] * y), $MachinePrecision] + 230661.510616), $MachinePrecision] * y), $MachinePrecision] + t), $MachinePrecision] / N[(N[(N[(N[(N[(N[(N[(y + a), $MachinePrecision] * y), $MachinePrecision] + b), $MachinePrecision] * y), $MachinePrecision] + c), $MachinePrecision] * y), $MachinePrecision] + i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, Infinity], t$95$1, N[((-N[(N[((-z) - N[((-a) * x), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]) + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x y) z) y) #s(literal 54929528941/2000000 binary64)) y) #s(literal 28832688827/125000 binary64)) y) t) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 y a) y) b) y) c) y) i)) < +inf.0

   1. Initial program 90.2%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

   if +inf.0 < (/.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x y) z) y) #s(literal 54929528941/2000000 binary64)) y) #s(literal 28832688827/125000 binary64)) y) t) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 y a) y) b) y) c) y) i))

   1. Initial program 0.0%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

   2. Taylor expanded in y around -inf

      \[\leadsto \color{blue}{x + -1 \cdot \frac{-1 \cdot z - -1 \cdot \left(a \cdot x\right)}{y}} \]
   3. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto -1 \cdot \frac{-1 \cdot z - -1 \cdot \left(a \cdot x\right)}{y} + \color{blue}{x} \]

      2. lower-+.f64 N/A

         \[\leadsto -1 \cdot \frac{-1 \cdot z - -1 \cdot \left(a \cdot x\right)}{y} + \color{blue}{x} \]

      3. mul-1-neg N/A

         \[\leadsto \left(\mathsf{neg}\left(\frac{-1 \cdot z - -1 \cdot \left(a \cdot x\right)}{y}\right)\right) + x \]

      4. lower-neg.f64 N/A

         \[\leadsto \left(-\frac{-1 \cdot z - -1 \cdot \left(a \cdot x\right)}{y}\right) + x \]

      5. lower-/.f64 N/A

         \[\leadsto \left(-\frac{-1 \cdot z - -1 \cdot \left(a \cdot x\right)}{y}\right) + x \]

      6. lower--.f64 N/A

         \[\leadsto \left(-\frac{-1 \cdot z - -1 \cdot \left(a \cdot x\right)}{y}\right) + x \]

      7. mul-1-neg N/A

         \[\leadsto \left(-\frac{\left(\mathsf{neg}\left(z\right)\right) - -1 \cdot \left(a \cdot x\right)}{y}\right) + x \]

      8. lower-neg.f64 N/A

         \[\leadsto \left(-\frac{\left(-z\right) - -1 \cdot \left(a \cdot x\right)}{y}\right) + x \]

      9. associate-*r* N/A

         \[\leadsto \left(-\frac{\left(-z\right) - \left(-1 \cdot a\right) \cdot x}{y}\right) + x \]

      10. mul-1-neg N/A

          \[\leadsto \left(-\frac{\left(-z\right) - \left(\mathsf{neg}\left(a\right)\right) \cdot x}{y}\right) + x \]

      11. lower-*.f64 N/A

          \[\leadsto \left(-\frac{\left(-z\right) - \left(\mathsf{neg}\left(a\right)\right) \cdot x}{y}\right) + x \]

      12. lower-neg.f64 69.6

          \[\leadsto \left(-\frac{\left(-z\right) - \left(-a\right) \cdot x}{y}\right) + x \]

   4. Applied rewrites 69.6%

      \[\leadsto \color{blue}{\left(-\frac{\left(-z\right) - \left(-a\right) \cdot x}{y}\right) + x} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 4: 75.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(-\frac{\left(-z\right) - \left(-a\right) \cdot x}{y}\right) + x\\ \mathbf{if}\;y \leq -1.05 \cdot 10^{+56}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{+57}:\\ \;\;\;\;\frac{\mathsf{fma}\left(\mathsf{fma}\left(27464.7644705, y, 230661.510616\right), y, t\right)}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (- (/ (- (- z) (* (- a) x)) y)) x)))
   (if (<= y -1.05e+56)
     t_1
     (if (<= y 1.9e+57)
       (/
        (fma (fma 27464.7644705 y 230661.510616) y t)
        (+ (* (+ (* (+ (* (+ y a) y) b) y) c) y) i))
       t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = -((-z - (-a * x)) / y) + x;
	double tmp;
	if (y <= -1.05e+56) {
		tmp = t_1;
	} else if (y <= 1.9e+57) {
		tmp = fma(fma(27464.7644705, y, 230661.510616), y, t) / (((((((y + a) * y) + b) * y) + c) * y) + i);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(-Float64(Float64(Float64(-z) - Float64(Float64(-a) * x)) / y)) + x)
	tmp = 0.0
	if (y <= -1.05e+56)
		tmp = t_1;
	elseif (y <= 1.9e+57)
		tmp = Float64(fma(fma(27464.7644705, y, 230661.510616), y, t) / Float64(Float64(Float64(Float64(Float64(Float64(Float64(y + a) * y) + b) * y) + c) * y) + i));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[((-N[(N[((-z) - N[((-a) * x), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]) + x), $MachinePrecision]}, If[LessEqual[y, -1.05e+56], t$95$1, If[LessEqual[y, 1.9e+57], N[(N[(N[(27464.7644705 * y + 230661.510616), $MachinePrecision] * y + t), $MachinePrecision] / N[(N[(N[(N[(N[(N[(N[(y + a), $MachinePrecision] * y), $MachinePrecision] + b), $MachinePrecision] * y), $MachinePrecision] + c), $MachinePrecision] * y), $MachinePrecision] + i), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.05000000000000009e56 or 1.8999999999999999e57 < y

   1. Initial program 1.9%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

   2. Taylor expanded in y around -inf

      \[\leadsto \color{blue}{x + -1 \cdot \frac{-1 \cdot z - -1 \cdot \left(a \cdot x\right)}{y}} \]
   3. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto -1 \cdot \frac{-1 \cdot z - -1 \cdot \left(a \cdot x\right)}{y} + \color{blue}{x} \]

      2. lower-+.f64 N/A

         \[\leadsto -1 \cdot \frac{-1 \cdot z - -1 \cdot \left(a \cdot x\right)}{y} + \color{blue}{x} \]

      3. mul-1-neg N/A

         \[\leadsto \left(\mathsf{neg}\left(\frac{-1 \cdot z - -1 \cdot \left(a \cdot x\right)}{y}\right)\right) + x \]

      4. lower-neg.f64 N/A

         \[\leadsto \left(-\frac{-1 \cdot z - -1 \cdot \left(a \cdot x\right)}{y}\right) + x \]

      5. lower-/.f64 N/A

         \[\leadsto \left(-\frac{-1 \cdot z - -1 \cdot \left(a \cdot x\right)}{y}\right) + x \]

      6. lower--.f64 N/A

         \[\leadsto \left(-\frac{-1 \cdot z - -1 \cdot \left(a \cdot x\right)}{y}\right) + x \]

      7. mul-1-neg N/A

         \[\leadsto \left(-\frac{\left(\mathsf{neg}\left(z\right)\right) - -1 \cdot \left(a \cdot x\right)}{y}\right) + x \]

      8. lower-neg.f64 N/A

         \[\leadsto \left(-\frac{\left(-z\right) - -1 \cdot \left(a \cdot x\right)}{y}\right) + x \]

      9. associate-*r* N/A

         \[\leadsto \left(-\frac{\left(-z\right) - \left(-1 \cdot a\right) \cdot x}{y}\right) + x \]

      10. mul-1-neg N/A

          \[\leadsto \left(-\frac{\left(-z\right) - \left(\mathsf{neg}\left(a\right)\right) \cdot x}{y}\right) + x \]

      11. lower-*.f64 N/A

          \[\leadsto \left(-\frac{\left(-z\right) - \left(\mathsf{neg}\left(a\right)\right) \cdot x}{y}\right) + x \]

      12. lower-neg.f64 68.4

          \[\leadsto \left(-\frac{\left(-z\right) - \left(-a\right) \cdot x}{y}\right) + x \]

   4. Applied rewrites 68.4%

      \[\leadsto \color{blue}{\left(-\frac{\left(-z\right) - \left(-a\right) \cdot x}{y}\right) + x} \]

   if -1.05000000000000009e56 < y < 1.8999999999999999e57

   1. Initial program 92.9%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

   2. Taylor expanded in y around 0

      \[\leadsto \frac{\color{blue}{t + y \cdot \left(\frac{28832688827}{125000} + \frac{54929528941}{2000000} \cdot y\right)}}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   3. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \frac{y \cdot \left(\frac{28832688827}{125000} + \frac{54929528941}{2000000} \cdot y\right) + \color{blue}{t}}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

      2. *-commutative N/A

         \[\leadsto \frac{\left(\frac{28832688827}{125000} + \frac{54929528941}{2000000} \cdot y\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

      3. lower-fma.f64 N/A

         \[\leadsto \frac{\mathsf{fma}\left(\frac{28832688827}{125000} + \frac{54929528941}{2000000} \cdot y, \color{blue}{y}, t\right)}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

      4. +-commutative N/A

         \[\leadsto \frac{\mathsf{fma}\left(\frac{54929528941}{2000000} \cdot y + \frac{28832688827}{125000}, y, t\right)}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

      5. lower-fma.f64 79.4

         \[\leadsto \frac{\mathsf{fma}\left(\mathsf{fma}\left(27464.7644705, y, 230661.510616\right), y, t\right)}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

   4. Applied rewrites 79.4%

      \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(27464.7644705, y, 230661.510616\right), y, t\right)}}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 5: 74.2% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(-\frac{\left(-z\right) - \left(-a\right) \cdot x}{y}\right) + x\\ \mathbf{if}\;y \leq -8.2 \cdot 10^{+55}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 3.3 \cdot 10^{+56}:\\ \;\;\;\;\frac{\mathsf{fma}\left(230661.510616, y, t\right)}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (- (/ (- (- z) (* (- a) x)) y)) x)))
   (if (<= y -8.2e+55)
     t_1
     (if (<= y 3.3e+56)
       (/ (fma 230661.510616 y t) (+ (* (+ (* (+ (* (+ y a) y) b) y) c) y) i))
       t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = -((-z - (-a * x)) / y) + x;
	double tmp;
	if (y <= -8.2e+55) {
		tmp = t_1;
	} else if (y <= 3.3e+56) {
		tmp = fma(230661.510616, y, t) / (((((((y + a) * y) + b) * y) + c) * y) + i);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(-Float64(Float64(Float64(-z) - Float64(Float64(-a) * x)) / y)) + x)
	tmp = 0.0
	if (y <= -8.2e+55)
		tmp = t_1;
	elseif (y <= 3.3e+56)
		tmp = Float64(fma(230661.510616, y, t) / Float64(Float64(Float64(Float64(Float64(Float64(Float64(y + a) * y) + b) * y) + c) * y) + i));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[((-N[(N[((-z) - N[((-a) * x), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]) + x), $MachinePrecision]}, If[LessEqual[y, -8.2e+55], t$95$1, If[LessEqual[y, 3.3e+56], N[(N[(230661.510616 * y + t), $MachinePrecision] / N[(N[(N[(N[(N[(N[(N[(y + a), $MachinePrecision] * y), $MachinePrecision] + b), $MachinePrecision] * y), $MachinePrecision] + c), $MachinePrecision] * y), $MachinePrecision] + i), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -8.19999999999999962e55 or 3.30000000000000002e56 < y

   1. Initial program 2.0%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

   2. Taylor expanded in y around -inf

      \[\leadsto \color{blue}{x + -1 \cdot \frac{-1 \cdot z - -1 \cdot \left(a \cdot x\right)}{y}} \]
   3. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto -1 \cdot \frac{-1 \cdot z - -1 \cdot \left(a \cdot x\right)}{y} + \color{blue}{x} \]

      2. lower-+.f64 N/A

         \[\leadsto -1 \cdot \frac{-1 \cdot z - -1 \cdot \left(a \cdot x\right)}{y} + \color{blue}{x} \]

      3. mul-1-neg N/A

         \[\leadsto \left(\mathsf{neg}\left(\frac{-1 \cdot z - -1 \cdot \left(a \cdot x\right)}{y}\right)\right) + x \]

      4. lower-neg.f64 N/A

         \[\leadsto \left(-\frac{-1 \cdot z - -1 \cdot \left(a \cdot x\right)}{y}\right) + x \]

      5. lower-/.f64 N/A

         \[\leadsto \left(-\frac{-1 \cdot z - -1 \cdot \left(a \cdot x\right)}{y}\right) + x \]

      6. lower--.f64 N/A

         \[\leadsto \left(-\frac{-1 \cdot z - -1 \cdot \left(a \cdot x\right)}{y}\right) + x \]

      7. mul-1-neg N/A

         \[\leadsto \left(-\frac{\left(\mathsf{neg}\left(z\right)\right) - -1 \cdot \left(a \cdot x\right)}{y}\right) + x \]

      8. lower-neg.f64 N/A

         \[\leadsto \left(-\frac{\left(-z\right) - -1 \cdot \left(a \cdot x\right)}{y}\right) + x \]

      9. associate-*r* N/A

         \[\leadsto \left(-\frac{\left(-z\right) - \left(-1 \cdot a\right) \cdot x}{y}\right) + x \]

      10. mul-1-neg N/A

          \[\leadsto \left(-\frac{\left(-z\right) - \left(\mathsf{neg}\left(a\right)\right) \cdot x}{y}\right) + x \]

      11. lower-*.f64 N/A

          \[\leadsto \left(-\frac{\left(-z\right) - \left(\mathsf{neg}\left(a\right)\right) \cdot x}{y}\right) + x \]

      12. lower-neg.f64 68.2

          \[\leadsto \left(-\frac{\left(-z\right) - \left(-a\right) \cdot x}{y}\right) + x \]

   4. Applied rewrites 68.2%

      \[\leadsto \color{blue}{\left(-\frac{\left(-z\right) - \left(-a\right) \cdot x}{y}\right) + x} \]

   if -8.19999999999999962e55 < y < 3.30000000000000002e56

   1. Initial program 93.1%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

   2. Taylor expanded in y around 0

      \[\leadsto \frac{\color{blue}{t + \frac{28832688827}{125000} \cdot y}}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   3. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \frac{\frac{28832688827}{125000} \cdot y + \color{blue}{t}}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

      2. lower-fma.f64 78.3

         \[\leadsto \frac{\mathsf{fma}\left(230661.510616, \color{blue}{y}, t\right)}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

   4. Applied rewrites 78.3%

      \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(230661.510616, y, t\right)}}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 6: 67.1% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(-\frac{\left(-z\right) - \left(-a\right) \cdot x}{y}\right) + x\\ \mathbf{if}\;y \leq -8.2 \cdot 10^{+55}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 3.3 \cdot 10^{+56}:\\ \;\;\;\;\frac{t}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(a + y, y, b\right), y, c\right), y, i\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (- (/ (- (- z) (* (- a) x)) y)) x)))
   (if (<= y -8.2e+55)
     t_1
     (if (<= y 3.3e+56) (/ t (fma (fma (fma (+ a y) y b) y c) y i)) t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = -((-z - (-a * x)) / y) + x;
	double tmp;
	if (y <= -8.2e+55) {
		tmp = t_1;
	} else if (y <= 3.3e+56) {
		tmp = t / fma(fma(fma((a + y), y, b), y, c), y, i);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(-Float64(Float64(Float64(-z) - Float64(Float64(-a) * x)) / y)) + x)
	tmp = 0.0
	if (y <= -8.2e+55)
		tmp = t_1;
	elseif (y <= 3.3e+56)
		tmp = Float64(t / fma(fma(fma(Float64(a + y), y, b), y, c), y, i));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[((-N[(N[((-z) - N[((-a) * x), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]) + x), $MachinePrecision]}, If[LessEqual[y, -8.2e+55], t$95$1, If[LessEqual[y, 3.3e+56], N[(t / N[(N[(N[(N[(a + y), $MachinePrecision] * y + b), $MachinePrecision] * y + c), $MachinePrecision] * y + i), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -8.19999999999999962e55 or 3.30000000000000002e56 < y

   1. Initial program 2.0%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

   2. Taylor expanded in y around -inf

      \[\leadsto \color{blue}{x + -1 \cdot \frac{-1 \cdot z - -1 \cdot \left(a \cdot x\right)}{y}} \]
   3. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto -1 \cdot \frac{-1 \cdot z - -1 \cdot \left(a \cdot x\right)}{y} + \color{blue}{x} \]

      2. lower-+.f64 N/A

         \[\leadsto -1 \cdot \frac{-1 \cdot z - -1 \cdot \left(a \cdot x\right)}{y} + \color{blue}{x} \]

      3. mul-1-neg N/A

         \[\leadsto \left(\mathsf{neg}\left(\frac{-1 \cdot z - -1 \cdot \left(a \cdot x\right)}{y}\right)\right) + x \]

      4. lower-neg.f64 N/A

         \[\leadsto \left(-\frac{-1 \cdot z - -1 \cdot \left(a \cdot x\right)}{y}\right) + x \]

      5. lower-/.f64 N/A

         \[\leadsto \left(-\frac{-1 \cdot z - -1 \cdot \left(a \cdot x\right)}{y}\right) + x \]

      6. lower--.f64 N/A

         \[\leadsto \left(-\frac{-1 \cdot z - -1 \cdot \left(a \cdot x\right)}{y}\right) + x \]

      7. mul-1-neg N/A

         \[\leadsto \left(-\frac{\left(\mathsf{neg}\left(z\right)\right) - -1 \cdot \left(a \cdot x\right)}{y}\right) + x \]

      8. lower-neg.f64 N/A

         \[\leadsto \left(-\frac{\left(-z\right) - -1 \cdot \left(a \cdot x\right)}{y}\right) + x \]

      9. associate-*r* N/A

         \[\leadsto \left(-\frac{\left(-z\right) - \left(-1 \cdot a\right) \cdot x}{y}\right) + x \]

      10. mul-1-neg N/A

          \[\leadsto \left(-\frac{\left(-z\right) - \left(\mathsf{neg}\left(a\right)\right) \cdot x}{y}\right) + x \]

      11. lower-*.f64 N/A

          \[\leadsto \left(-\frac{\left(-z\right) - \left(\mathsf{neg}\left(a\right)\right) \cdot x}{y}\right) + x \]

      12. lower-neg.f64 68.2

          \[\leadsto \left(-\frac{\left(-z\right) - \left(-a\right) \cdot x}{y}\right) + x \]

   4. Applied rewrites 68.2%

      \[\leadsto \color{blue}{\left(-\frac{\left(-z\right) - \left(-a\right) \cdot x}{y}\right) + x} \]

   if -8.19999999999999962e55 < y < 3.30000000000000002e56

   1. Initial program 93.1%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

   2. Taylor expanded in t around inf

      \[\leadsto \color{blue}{\frac{t}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}} \]
   3. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \frac{t}{\color{blue}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}} \]

      2. +-commutative N/A

         \[\leadsto \frac{t}{y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right) + \color{blue}{i}} \]

      3. *-commutative N/A

         \[\leadsto \frac{t}{\left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right) \cdot y + i} \]

      4. lower-fma.f64 N/A

         \[\leadsto \frac{t}{\mathsf{fma}\left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right), \color{blue}{y}, i\right)} \]

      5. +-commutative N/A

         \[\leadsto \frac{t}{\mathsf{fma}\left(y \cdot \left(b + y \cdot \left(a + y\right)\right) + c, y, i\right)} \]

      6. *-commutative N/A

         \[\leadsto \frac{t}{\mathsf{fma}\left(\left(b + y \cdot \left(a + y\right)\right) \cdot y + c, y, i\right)} \]

      7. +-commutative N/A

         \[\leadsto \frac{t}{\mathsf{fma}\left(\left(b + y \cdot \left(y + a\right)\right) \cdot y + c, y, i\right)} \]

      8. *-commutative N/A

         \[\leadsto \frac{t}{\mathsf{fma}\left(\left(b + \left(y + a\right) \cdot y\right) \cdot y + c, y, i\right)} \]

      9. +-commutative N/A

         \[\leadsto \frac{t}{\mathsf{fma}\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c, y, i\right)} \]

      10. lower-fma.f64 N/A

          \[\leadsto \frac{t}{\mathsf{fma}\left(\mathsf{fma}\left(\left(y + a\right) \cdot y + b, y, c\right), y, i\right)} \]

      11. lower-fma.f64 N/A

          \[\leadsto \frac{t}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(y + a, y, b\right), y, c\right), y, i\right)} \]

      12. +-commutative N/A

          \[\leadsto \frac{t}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(a + y, y, b\right), y, c\right), y, i\right)} \]

      13. lower-+.f64 66.4

          \[\leadsto \frac{t}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(a + y, y, b\right), y, c\right), y, i\right)} \]

   4. Applied rewrites 66.4%

      \[\leadsto \color{blue}{\frac{t}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(a + y, y, b\right), y, c\right), y, i\right)}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 7: 64.4% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(-\frac{\left(-z\right) - \left(-a\right) \cdot x}{y}\right) + x\\ \mathbf{if}\;y \leq -2.9 \cdot 10^{+50}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 0.0048:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{230661.510616}{i}, \frac{t}{\mathsf{fma}\left(c, y, i\right)}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (- (/ (- (- z) (* (- a) x)) y)) x)))
   (if (<= y -2.9e+50)
     t_1
     (if (<= y 0.0048) (fma y (/ 230661.510616 i) (/ t (fma c y i))) t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = -((-z - (-a * x)) / y) + x;
	double tmp;
	if (y <= -2.9e+50) {
		tmp = t_1;
	} else if (y <= 0.0048) {
		tmp = fma(y, (230661.510616 / i), (t / fma(c, y, i)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(-Float64(Float64(Float64(-z) - Float64(Float64(-a) * x)) / y)) + x)
	tmp = 0.0
	if (y <= -2.9e+50)
		tmp = t_1;
	elseif (y <= 0.0048)
		tmp = fma(y, Float64(230661.510616 / i), Float64(t / fma(c, y, i)));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[((-N[(N[((-z) - N[((-a) * x), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]) + x), $MachinePrecision]}, If[LessEqual[y, -2.9e+50], t$95$1, If[LessEqual[y, 0.0048], N[(y * N[(230661.510616 / i), $MachinePrecision] + N[(t / N[(c * y + i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -2.9e50 or 0.00479999999999999958 < y

   1. Initial program 8.5%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

   2. Taylor expanded in y around -inf

      \[\leadsto \color{blue}{x + -1 \cdot \frac{-1 \cdot z - -1 \cdot \left(a \cdot x\right)}{y}} \]
   3. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto -1 \cdot \frac{-1 \cdot z - -1 \cdot \left(a \cdot x\right)}{y} + \color{blue}{x} \]

      2. lower-+.f64 N/A

         \[\leadsto -1 \cdot \frac{-1 \cdot z - -1 \cdot \left(a \cdot x\right)}{y} + \color{blue}{x} \]

      3. mul-1-neg N/A

         \[\leadsto \left(\mathsf{neg}\left(\frac{-1 \cdot z - -1 \cdot \left(a \cdot x\right)}{y}\right)\right) + x \]

      4. lower-neg.f64 N/A

         \[\leadsto \left(-\frac{-1 \cdot z - -1 \cdot \left(a \cdot x\right)}{y}\right) + x \]

      5. lower-/.f64 N/A

         \[\leadsto \left(-\frac{-1 \cdot z - -1 \cdot \left(a \cdot x\right)}{y}\right) + x \]

      6. lower--.f64 N/A

         \[\leadsto \left(-\frac{-1 \cdot z - -1 \cdot \left(a \cdot x\right)}{y}\right) + x \]

      7. mul-1-neg N/A

         \[\leadsto \left(-\frac{\left(\mathsf{neg}\left(z\right)\right) - -1 \cdot \left(a \cdot x\right)}{y}\right) + x \]

      8. lower-neg.f64 N/A

         \[\leadsto \left(-\frac{\left(-z\right) - -1 \cdot \left(a \cdot x\right)}{y}\right) + x \]

      9. associate-*r* N/A

         \[\leadsto \left(-\frac{\left(-z\right) - \left(-1 \cdot a\right) \cdot x}{y}\right) + x \]

      10. mul-1-neg N/A

          \[\leadsto \left(-\frac{\left(-z\right) - \left(\mathsf{neg}\left(a\right)\right) \cdot x}{y}\right) + x \]

      11. lower-*.f64 N/A

          \[\leadsto \left(-\frac{\left(-z\right) - \left(\mathsf{neg}\left(a\right)\right) \cdot x}{y}\right) + x \]

      12. lower-neg.f64 61.8

          \[\leadsto \left(-\frac{\left(-z\right) - \left(-a\right) \cdot x}{y}\right) + x \]

   4. Applied rewrites 61.8%

      \[\leadsto \color{blue}{\left(-\frac{\left(-z\right) - \left(-a\right) \cdot x}{y}\right) + x} \]

   if -2.9e50 < y < 0.00479999999999999958

   1. Initial program 96.8%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

   3. Applied rewrites 96.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(y, x, z\right), y, 27464.7644705\right), y, 230661.510616\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(a + y, y, b\right), y, c\right), y, i\right)}, \frac{t}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(a + y, y, b\right), y, c\right), y, i\right)}\right)} \]

   4. Taylor expanded in y around 0

      \[\leadsto \mathsf{fma}\left(y, \color{blue}{\frac{\frac{28832688827}{125000}}{i}}, \frac{t}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(a + y, y, b\right), y, c\right), y, i\right)}\right) \]
   5. Step-by-step derivation

      1. lower-/.f64 70.2

         \[\leadsto \mathsf{fma}\left(y, \frac{230661.510616}{\color{blue}{i}}, \frac{t}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(a + y, y, b\right), y, c\right), y, i\right)}\right) \]

   6. Applied rewrites 70.2%

      \[\leadsto \mathsf{fma}\left(y, \color{blue}{\frac{230661.510616}{i}}, \frac{t}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(a + y, y, b\right), y, c\right), y, i\right)}\right) \]

   7. Taylor expanded in y around 0

      \[\leadsto \mathsf{fma}\left(y, \frac{\frac{28832688827}{125000}}{i}, \frac{t}{\mathsf{fma}\left(\color{blue}{c}, y, i\right)}\right) \]
   8. Step-by-step derivation

   9. Applied rewrites 66.6%

      \[\leadsto \mathsf{fma}\left(y, \frac{230661.510616}{i}, \frac{t}{\mathsf{fma}\left(\color{blue}{c}, y, i\right)}\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 8: 59.6% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(-\frac{\left(-z\right) - \left(-a\right) \cdot x}{y}\right) + x\\ \mathbf{if}\;y \leq -1.4 \cdot 10^{+55}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{+49}:\\ \;\;\;\;\frac{t}{\mathsf{fma}\left(y \cdot y, \mathsf{fma}\left(a, y, b\right), i\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (- (/ (- (- z) (* (- a) x)) y)) x)))
   (if (<= y -1.4e+55)
     t_1
     (if (<= y 1.2e+49) (/ t (fma (* y y) (fma a y b) i)) t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = -((-z - (-a * x)) / y) + x;
	double tmp;
	if (y <= -1.4e+55) {
		tmp = t_1;
	} else if (y <= 1.2e+49) {
		tmp = t / fma((y * y), fma(a, y, b), i);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(-Float64(Float64(Float64(-z) - Float64(Float64(-a) * x)) / y)) + x)
	tmp = 0.0
	if (y <= -1.4e+55)
		tmp = t_1;
	elseif (y <= 1.2e+49)
		tmp = Float64(t / fma(Float64(y * y), fma(a, y, b), i));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[((-N[(N[((-z) - N[((-a) * x), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]) + x), $MachinePrecision]}, If[LessEqual[y, -1.4e+55], t$95$1, If[LessEqual[y, 1.2e+49], N[(t / N[(N[(y * y), $MachinePrecision] * N[(a * y + b), $MachinePrecision] + i), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.4e55 or 1.2e49 < y

   1. Initial program 2.5%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

   2. Taylor expanded in y around -inf

      \[\leadsto \color{blue}{x + -1 \cdot \frac{-1 \cdot z - -1 \cdot \left(a \cdot x\right)}{y}} \]
   3. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto -1 \cdot \frac{-1 \cdot z - -1 \cdot \left(a \cdot x\right)}{y} + \color{blue}{x} \]

      2. lower-+.f64 N/A

         \[\leadsto -1 \cdot \frac{-1 \cdot z - -1 \cdot \left(a \cdot x\right)}{y} + \color{blue}{x} \]

      3. mul-1-neg N/A

         \[\leadsto \left(\mathsf{neg}\left(\frac{-1 \cdot z - -1 \cdot \left(a \cdot x\right)}{y}\right)\right) + x \]

      4. lower-neg.f64 N/A

         \[\leadsto \left(-\frac{-1 \cdot z - -1 \cdot \left(a \cdot x\right)}{y}\right) + x \]

      5. lower-/.f64 N/A

         \[\leadsto \left(-\frac{-1 \cdot z - -1 \cdot \left(a \cdot x\right)}{y}\right) + x \]

      6. lower--.f64 N/A

         \[\leadsto \left(-\frac{-1 \cdot z - -1 \cdot \left(a \cdot x\right)}{y}\right) + x \]

      7. mul-1-neg N/A

         \[\leadsto \left(-\frac{\left(\mathsf{neg}\left(z\right)\right) - -1 \cdot \left(a \cdot x\right)}{y}\right) + x \]

      8. lower-neg.f64 N/A

         \[\leadsto \left(-\frac{\left(-z\right) - -1 \cdot \left(a \cdot x\right)}{y}\right) + x \]

      9. associate-*r* N/A

         \[\leadsto \left(-\frac{\left(-z\right) - \left(-1 \cdot a\right) \cdot x}{y}\right) + x \]

      10. mul-1-neg N/A

          \[\leadsto \left(-\frac{\left(-z\right) - \left(\mathsf{neg}\left(a\right)\right) \cdot x}{y}\right) + x \]

      11. lower-*.f64 N/A

          \[\leadsto \left(-\frac{\left(-z\right) - \left(\mathsf{neg}\left(a\right)\right) \cdot x}{y}\right) + x \]

      12. lower-neg.f64 67.5

          \[\leadsto \left(-\frac{\left(-z\right) - \left(-a\right) \cdot x}{y}\right) + x \]

   4. Applied rewrites 67.5%

      \[\leadsto \color{blue}{\left(-\frac{\left(-z\right) - \left(-a\right) \cdot x}{y}\right) + x} \]

   if -1.4e55 < y < 1.2e49

   1. Initial program 93.8%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

   2. Taylor expanded in c around 0

      \[\leadsto \color{blue}{\frac{t + y \cdot \left(\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot \left(z + x \cdot y\right)\right)\right)}{i + {y}^{2} \cdot \left(b + y \cdot \left(a + y\right)\right)}} \]
   3. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \frac{t + y \cdot \left(\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot \left(z + x \cdot y\right)\right)\right)}{\color{blue}{i + {y}^{2} \cdot \left(b + y \cdot \left(a + y\right)\right)}} \]

   4. Applied rewrites 72.9%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(y, x, z\right), y, 27464.7644705\right), y, 230661.510616\right), y, t\right)}{\mathsf{fma}\left(y \cdot y, \mathsf{fma}\left(a + y, y, b\right), i\right)}} \]

   5. Taylor expanded in y around 0

      \[\leadsto \frac{t}{\mathsf{fma}\left(\color{blue}{y \cdot y}, \mathsf{fma}\left(a + y, y, b\right), i\right)} \]
   6. Step-by-step derivation

   7. Applied rewrites 54.0%

      \[\leadsto \frac{t}{\mathsf{fma}\left(\color{blue}{y \cdot y}, \mathsf{fma}\left(a + y, y, b\right), i\right)} \]

   8. Taylor expanded in y around 0

      \[\leadsto \frac{t}{\mathsf{fma}\left(y \cdot y, \mathsf{fma}\left(a, y, b\right), i\right)} \]
   9. Step-by-step derivation

   10. Applied rewrites 53.6%

       \[\leadsto \frac{t}{\mathsf{fma}\left(y \cdot y, \mathsf{fma}\left(a, y, b\right), i\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 9: 59.3% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(-\frac{\left(-z\right) - \left(-a\right) \cdot x}{y}\right) + x\\ \mathbf{if}\;y \leq -2.9 \cdot 10^{+50}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 0.0048:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{230661.510616}{i}, \frac{t}{i}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (- (/ (- (- z) (* (- a) x)) y)) x)))
   (if (<= y -2.9e+50)
     t_1
     (if (<= y 0.0048) (fma y (/ 230661.510616 i) (/ t i)) t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = -((-z - (-a * x)) / y) + x;
	double tmp;
	if (y <= -2.9e+50) {
		tmp = t_1;
	} else if (y <= 0.0048) {
		tmp = fma(y, (230661.510616 / i), (t / i));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(-Float64(Float64(Float64(-z) - Float64(Float64(-a) * x)) / y)) + x)
	tmp = 0.0
	if (y <= -2.9e+50)
		tmp = t_1;
	elseif (y <= 0.0048)
		tmp = fma(y, Float64(230661.510616 / i), Float64(t / i));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[((-N[(N[((-z) - N[((-a) * x), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]) + x), $MachinePrecision]}, If[LessEqual[y, -2.9e+50], t$95$1, If[LessEqual[y, 0.0048], N[(y * N[(230661.510616 / i), $MachinePrecision] + N[(t / i), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -2.9e50 or 0.00479999999999999958 < y

   1. Initial program 8.5%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

   2. Taylor expanded in y around -inf

      \[\leadsto \color{blue}{x + -1 \cdot \frac{-1 \cdot z - -1 \cdot \left(a \cdot x\right)}{y}} \]
   3. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto -1 \cdot \frac{-1 \cdot z - -1 \cdot \left(a \cdot x\right)}{y} + \color{blue}{x} \]

      2. lower-+.f64 N/A

         \[\leadsto -1 \cdot \frac{-1 \cdot z - -1 \cdot \left(a \cdot x\right)}{y} + \color{blue}{x} \]

      3. mul-1-neg N/A

         \[\leadsto \left(\mathsf{neg}\left(\frac{-1 \cdot z - -1 \cdot \left(a \cdot x\right)}{y}\right)\right) + x \]

      4. lower-neg.f64 N/A

         \[\leadsto \left(-\frac{-1 \cdot z - -1 \cdot \left(a \cdot x\right)}{y}\right) + x \]

      5. lower-/.f64 N/A

         \[\leadsto \left(-\frac{-1 \cdot z - -1 \cdot \left(a \cdot x\right)}{y}\right) + x \]

      6. lower--.f64 N/A

         \[\leadsto \left(-\frac{-1 \cdot z - -1 \cdot \left(a \cdot x\right)}{y}\right) + x \]

      7. mul-1-neg N/A

         \[\leadsto \left(-\frac{\left(\mathsf{neg}\left(z\right)\right) - -1 \cdot \left(a \cdot x\right)}{y}\right) + x \]

      8. lower-neg.f64 N/A

         \[\leadsto \left(-\frac{\left(-z\right) - -1 \cdot \left(a \cdot x\right)}{y}\right) + x \]

      9. associate-*r* N/A

         \[\leadsto \left(-\frac{\left(-z\right) - \left(-1 \cdot a\right) \cdot x}{y}\right) + x \]

      10. mul-1-neg N/A

          \[\leadsto \left(-\frac{\left(-z\right) - \left(\mathsf{neg}\left(a\right)\right) \cdot x}{y}\right) + x \]

      11. lower-*.f64 N/A

          \[\leadsto \left(-\frac{\left(-z\right) - \left(\mathsf{neg}\left(a\right)\right) \cdot x}{y}\right) + x \]

      12. lower-neg.f64 61.8

          \[\leadsto \left(-\frac{\left(-z\right) - \left(-a\right) \cdot x}{y}\right) + x \]

   4. Applied rewrites 61.8%

      \[\leadsto \color{blue}{\left(-\frac{\left(-z\right) - \left(-a\right) \cdot x}{y}\right) + x} \]

   if -2.9e50 < y < 0.00479999999999999958

   1. Initial program 96.8%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

   3. Applied rewrites 96.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(y, x, z\right), y, 27464.7644705\right), y, 230661.510616\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(a + y, y, b\right), y, c\right), y, i\right)}, \frac{t}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(a + y, y, b\right), y, c\right), y, i\right)}\right)} \]

   4. Taylor expanded in y around 0

      \[\leadsto \mathsf{fma}\left(y, \color{blue}{\frac{\frac{28832688827}{125000}}{i}}, \frac{t}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(a + y, y, b\right), y, c\right), y, i\right)}\right) \]
   5. Step-by-step derivation

      1. lower-/.f64 70.2

         \[\leadsto \mathsf{fma}\left(y, \frac{230661.510616}{\color{blue}{i}}, \frac{t}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(a + y, y, b\right), y, c\right), y, i\right)}\right) \]

   6. Applied rewrites 70.2%

      \[\leadsto \mathsf{fma}\left(y, \color{blue}{\frac{230661.510616}{i}}, \frac{t}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(a + y, y, b\right), y, c\right), y, i\right)}\right) \]

   7. Taylor expanded in y around 0

      \[\leadsto \mathsf{fma}\left(y, \frac{\frac{28832688827}{125000}}{i}, \frac{t}{\color{blue}{i}}\right) \]
   8. Step-by-step derivation

   9. Applied rewrites 57.8%

      \[\leadsto \mathsf{fma}\left(y, \frac{230661.510616}{i}, \frac{t}{\color{blue}{i}}\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 10: 54.9% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2650:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 0.0048:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{230661.510616}{i}, \frac{t}{i}\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y -2650.0)
   x
   (if (<= y 0.0048) (fma y (/ 230661.510616 i) (/ t i)) x)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= -2650.0) {
		tmp = x;
	} else if (y <= 0.0048) {
		tmp = fma(y, (230661.510616 / i), (t / i));
	} else {
		tmp = x;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= -2650.0)
		tmp = x;
	elseif (y <= 0.0048)
		tmp = fma(y, Float64(230661.510616 / i), Float64(t / i));
	else
		tmp = x;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, -2650.0], x, If[LessEqual[y, 0.0048], N[(y * N[(230661.510616 / i), $MachinePrecision] + N[(t / i), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if y < -2650 or 0.00479999999999999958 < y

   1. Initial program 12.2%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

   2. Taylor expanded in y around inf

      \[\leadsto \color{blue}{x} \]
   3. Step-by-step derivation

   4. Applied rewrites 47.8%

      \[\leadsto \color{blue}{x} \]

   if -2650 < y < 0.00479999999999999958

   1. Initial program 99.7%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

   3. Applied rewrites 99.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(y, x, z\right), y, 27464.7644705\right), y, 230661.510616\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(a + y, y, b\right), y, c\right), y, i\right)}, \frac{t}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(a + y, y, b\right), y, c\right), y, i\right)}\right)} \]

   4. Taylor expanded in y around 0

      \[\leadsto \mathsf{fma}\left(y, \color{blue}{\frac{\frac{28832688827}{125000}}{i}}, \frac{t}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(a + y, y, b\right), y, c\right), y, i\right)}\right) \]
   5. Step-by-step derivation

      1. lower-/.f64 74.9

         \[\leadsto \mathsf{fma}\left(y, \frac{230661.510616}{\color{blue}{i}}, \frac{t}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(a + y, y, b\right), y, c\right), y, i\right)}\right) \]

   6. Applied rewrites 74.9%

      \[\leadsto \mathsf{fma}\left(y, \color{blue}{\frac{230661.510616}{i}}, \frac{t}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(a + y, y, b\right), y, c\right), y, i\right)}\right) \]

   7. Taylor expanded in y around 0

      \[\leadsto \mathsf{fma}\left(y, \frac{\frac{28832688827}{125000}}{i}, \frac{t}{\color{blue}{i}}\right) \]
   8. Step-by-step derivation

   9. Applied rewrites 61.8%

      \[\leadsto \mathsf{fma}\left(y, \frac{230661.510616}{i}, \frac{t}{\color{blue}{i}}\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 11: 54.8% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2650:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 0.0048:\\ \;\;\;\;\mathsf{fma}\left(230661.510616, \frac{y}{i}, \frac{t}{i}\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y -2650.0)
   x
   (if (<= y 0.0048) (fma 230661.510616 (/ y i) (/ t i)) x)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= -2650.0) {
		tmp = x;
	} else if (y <= 0.0048) {
		tmp = fma(230661.510616, (y / i), (t / i));
	} else {
		tmp = x;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= -2650.0)
		tmp = x;
	elseif (y <= 0.0048)
		tmp = fma(230661.510616, Float64(y / i), Float64(t / i));
	else
		tmp = x;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, -2650.0], x, If[LessEqual[y, 0.0048], N[(230661.510616 * N[(y / i), $MachinePrecision] + N[(t / i), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if y < -2650 or 0.00479999999999999958 < y

   1. Initial program 12.2%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

   2. Taylor expanded in y around inf

      \[\leadsto \color{blue}{x} \]
   3. Step-by-step derivation

   4. Applied rewrites 47.8%

      \[\leadsto \color{blue}{x} \]

   if -2650 < y < 0.00479999999999999958

   1. Initial program 99.7%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

   2. Taylor expanded in c around 0

      \[\leadsto \color{blue}{\frac{t + y \cdot \left(\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot \left(z + x \cdot y\right)\right)\right)}{i + {y}^{2} \cdot \left(b + y \cdot \left(a + y\right)\right)}} \]
   3. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \frac{t + y \cdot \left(\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot \left(z + x \cdot y\right)\right)\right)}{\color{blue}{i + {y}^{2} \cdot \left(b + y \cdot \left(a + y\right)\right)}} \]

   4. Applied rewrites 77.3%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(y, x, z\right), y, 27464.7644705\right), y, 230661.510616\right), y, t\right)}{\mathsf{fma}\left(y \cdot y, \mathsf{fma}\left(a + y, y, b\right), i\right)}} \]

   5. Taylor expanded in y around 0

      \[\leadsto \frac{28832688827}{125000} \cdot \frac{y}{i} + \color{blue}{\frac{t}{i}} \]
   6. Step-by-step derivation

      1. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(\frac{28832688827}{125000}, \frac{y}{\color{blue}{i}}, \frac{t}{i}\right) \]

      2. lower-/.f64 N/A

         \[\leadsto \mathsf{fma}\left(\frac{28832688827}{125000}, \frac{y}{i}, \frac{t}{i}\right) \]

      3. lower-/.f64 61.8

         \[\leadsto \mathsf{fma}\left(230661.510616, \frac{y}{i}, \frac{t}{i}\right) \]

   7. Applied rewrites 61.8%

      \[\leadsto \mathsf{fma}\left(230661.510616, \color{blue}{\frac{y}{i}}, \frac{t}{i}\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 12: 53.1% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.4 \cdot 10^{+56}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{+64}:\\ \;\;\;\;\frac{t}{\mathsf{fma}\left(y \cdot y, b, i\right)}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y -3.4e+56) x (if (<= y 6.5e+64) (/ t (fma (* y y) b i)) x)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= -3.4e+56) {
		tmp = x;
	} else if (y <= 6.5e+64) {
		tmp = t / fma((y * y), b, i);
	} else {
		tmp = x;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= -3.4e+56)
		tmp = x;
	elseif (y <= 6.5e+64)
		tmp = Float64(t / fma(Float64(y * y), b, i));
	else
		tmp = x;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, -3.4e+56], x, If[LessEqual[y, 6.5e+64], N[(t / N[(N[(y * y), $MachinePrecision] * b + i), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if y < -3.40000000000000001e56 or 6.50000000000000007e64 < y

   1. Initial program 1.6%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

   2. Taylor expanded in y around inf

      \[\leadsto \color{blue}{x} \]
   3. Step-by-step derivation

   4. Applied rewrites 57.1%

      \[\leadsto \color{blue}{x} \]

   if -3.40000000000000001e56 < y < 6.50000000000000007e64

   1. Initial program 92.1%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

   2. Taylor expanded in c around 0

      \[\leadsto \color{blue}{\frac{t + y \cdot \left(\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot \left(z + x \cdot y\right)\right)\right)}{i + {y}^{2} \cdot \left(b + y \cdot \left(a + y\right)\right)}} \]
   3. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \frac{t + y \cdot \left(\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot \left(z + x \cdot y\right)\right)\right)}{\color{blue}{i + {y}^{2} \cdot \left(b + y \cdot \left(a + y\right)\right)}} \]

   4. Applied rewrites 71.7%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(y, x, z\right), y, 27464.7644705\right), y, 230661.510616\right), y, t\right)}{\mathsf{fma}\left(y \cdot y, \mathsf{fma}\left(a + y, y, b\right), i\right)}} \]

   5. Taylor expanded in y around 0

      \[\leadsto \frac{t}{\mathsf{fma}\left(\color{blue}{y \cdot y}, \mathsf{fma}\left(a + y, y, b\right), i\right)} \]
   6. Step-by-step derivation

   7. Applied rewrites 52.9%

      \[\leadsto \frac{t}{\mathsf{fma}\left(\color{blue}{y \cdot y}, \mathsf{fma}\left(a + y, y, b\right), i\right)} \]

   8. Taylor expanded in y around 0

      \[\leadsto \frac{t}{\mathsf{fma}\left(y \cdot y, b, i\right)} \]
   9. Step-by-step derivation

   10. Applied rewrites 50.5%

       \[\leadsto \frac{t}{\mathsf{fma}\left(y \cdot y, b, i\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 13: 51.1% accurate, 3.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2650:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{+64}:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y -2650.0) x (if (<= y 6.5e+64) (/ t i) x)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= -2650.0) {
		tmp = x;
	} else if (y <= 6.5e+64) {
		tmp = t / i;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a, b, c, i)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (y <= (-2650.0d0)) then
        tmp = x
    else if (y <= 6.5d+64) then
        tmp = t / i
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= -2650.0) {
		tmp = x;
	} else if (y <= 6.5e+64) {
		tmp = t / i;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= -2650.0:
		tmp = x
	elif y <= 6.5e+64:
		tmp = t / i
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= -2650.0)
		tmp = x;
	elseif (y <= 6.5e+64)
		tmp = Float64(t / i);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (y <= -2650.0)
		tmp = x;
	elseif (y <= 6.5e+64)
		tmp = t / i;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, -2650.0], x, If[LessEqual[y, 6.5e+64], N[(t / i), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if y < -2650 or 6.50000000000000007e64 < y

   1. Initial program 6.8%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

   2. Taylor expanded in y around inf

      \[\leadsto \color{blue}{x} \]
   3. Step-by-step derivation

   4. Applied rewrites 52.4%

      \[\leadsto \color{blue}{x} \]

   if -2650 < y < 6.50000000000000007e64

   1. Initial program 95.0%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

   2. Taylor expanded in y around 0

      \[\leadsto \color{blue}{\frac{t}{i}} \]
   3. Step-by-step derivation

      1. lower-/.f64 50.1

         \[\leadsto \frac{t}{\color{blue}{i}} \]

   4. Applied rewrites 50.1%

      \[\leadsto \color{blue}{\frac{t}{i}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 14: 25.6% accurate, 46.9× speedup

Math

\[\begin{array}{l} \\ x \end{array} \]

FPCore

(FPCore (x y z t a b c i) :precision binary64 x)

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	return x;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a, b, c, i)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    code = x
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	return x;
}

Python

def code(x, y, z, t, a, b, c, i):
	return x

Julia

function code(x, y, z, t, a, b, c, i)
	return x
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i)
	tmp = x;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := x

Derivation

1. Initial program 56.2%

   \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

2. Taylor expanded in y around inf

   \[\leadsto \color{blue}{x} \]
3. Step-by-step derivation

4. Applied rewrites 25.6%

   \[\leadsto \color{blue}{x} \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2025115 
(FPCore (x y z t a b c i)
  :name "Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2"
  :precision binary64
  (/ (+ (* (+ (* (+ (* (+ (* x y) z) y) 27464.7644705) y) 230661.510616) y) t) (+ (* (+ (* (+ (* (+ y a) y) b) y) c) y) i)))